Not saying any of these are the best, just the best of the ones I have downloaded...
Free Apps
thetrainline- checks next train times without requiring to pay the £5 for the National Rail Enquiries App
Shazam Free- identify songs that are playing (in a pub etc), can only do 5 per month in the free one but I never use more anyway
Facebook- if you are into that kind of thing
Sky Sports Football Score Centre- pretty good for football scores
Flixster- check movie times and listings
Wikipanion- Wikipedia lookup
TV Guide- self explanatory!
Whirly Word Free- anagram game, only difference between it and the paid version is adverts you barely notice
Words With Friends Free- Scrabble-a-like, play against friends or random folk over the internet (there is a chess equivalent too if you like that)
Paid for
TuneIn Radio- internet radio app
Flight Control- very addictive "air traffic control" game, would highly recommend for 59p
Angry Birds- never liked it that much myself but try the demo and it is only 59p
Tiger Woods PGA Tour- only 59p at the moment, quite easy once you get into it but I really like it
Doodle Jump- good for a wee blast while waiting on the train and only 59p
Not Quite An App As Such
In the internet browser go to iphone.tvcatchup.com and create an account to stream uk freeview tv
Hope that helps!